Utility-Scale Quantum Computation of Ground-State Energy in a 100+ Site Planar Kagome Antiferromagnet via Hamiltonian Engineering

Abstract: We present experimental quantum computation of the ground-state energy in a 103-site flat Kagome lattice under the antiferromagnetic Heisenberg model (KAFH), with IBM's Heron r1 and Heron r2 quantum processors. For spin-1/2 KAFH, our per-site ground-state energy estimate is $-0.417\,J$, which, under open-boundary corrections, matches the energy in the thermodynamic limit, i.e., $-0.4386\,J$. To achieve this, we used a hybrid approach that splits the conventional Variational Quantum Eigensolver (VQE) into local (classical) and global (quantum) components for efficient hardware utilization. More importantly, we introduce a Hamiltonian engineering strategy that increases coupling on defect triangles to mimic loop-flip dynamics, allowing us to simplify the ansatz while retaining computational accuracy. Using a single-repetition, hardware-efficient ansatz, we entangle up to 103 qubits with high fidelity to determine the Hamiltonian's lowest eigenvalue. This work demonstrates the scalability of VQE for frustrated 2D systems and lays the foundation for future studies using deeper ansatz circuits and larger lattices on utility quantum processors.

• The paper demonstrates a novel Hamiltonian engineering approach that enhances VQE performance for computing the ground-state energy in a 103-site Kagome antiferromagnet.
• The methodology partitions the simulation into local and global VQE phases, optimizing subcircuits and junction parameters to efficiently mitigate noise.
• Experimental results from IBM’s Heron processor closely model theoretical predictions despite finite-size effects, validating the approach for complex, frustrated spin systems.

Utility-Scale Quantum Computation of Ground-State Energy in a 100+ Site Planar Kagome Antiferromagnet via Hamiltonian Engineering

Introduction

The study focuses on the application of quantum computation to determine the ground-state energy of a 103-site planar Kagome lattice antiferromagnet using variational quantum eigensolver (VQE) techniques. The Kagome lattice, notable for its intrinsic geometric frustration, is an ideal candidate for exploring exotic quantum phases such as quantum spin liquids. The paper reports a per-site ground-state energy estimate close to theoretical values in the thermodynamic limit and introduces a novel Hamiltonian engineering approach to optimize quantum resources.

Hamiltonian Engineering Strategy

A central innovation in this study is the Hamiltonian engineering technique applied to defect triangles within the lattice. Specifically, bond strengths on defect triangles are increased beyond the uniform coupling constant $J$ to $J' \approx 2J$, enabling the simulation of loop-flip dynamics. This modification effectively enhances dimer resonance and local quantum fluctuations, aligning the system closer to resonating valence bond (RVB) states. The method involves calibrating $J'$ to match known small-scale results from exact diagonalization, presenting a scalable approach adaptable to larger lattices.

VQE Framework

The VQE implementation partitions the problem into local and global optimization phases:

1. Local VQE: This phase optimizes parameters for subcircuits (15-19 qubits) corresponding to distinct lattice segments. These subcircuits are independently optimized on classical hardware, yielding local ground-state energies and parameterized single-qubit rotation configurations.
2. Global VQE: Reconstructing a global ansatz involves concatenating optimized local segments and fine-tuning junction qubit parameters on quantum hardware. The aim is to minimize noise and build on long-range entanglement by adjusting only junction parameters, making the method resource-efficient while preserving the integrity of the Kagome lattice's topology.

Noise Mitigation and Optimization

The study employs Operator Decoherence Renormalization (ODR) for noise mitigation. This post-processing step refines the energy estimates by comparing output from a specific, classically simulable quantum state configuration to the anticipated noisy state. The ODR significantly reduces the effect of hardware noise and statistical fluctuations, allowing more reliable results from current quantum hardware.

Experimental Results

Experimental results on IBM's Heron quantum processors demonstrate that the method achieves an average ground-state energy that models the theoretical predictions, albeit slightly higher due to finite-size effects. The expected ground-state energy per site for the Kagome lattice in the thermodynamic limit is approximately $-0.4386J$, while the experimentally determined value is $-0.417J$. This discrepancy is attributed to open boundary conditions and edge effects, which are considered in the analysis.

Implications and Future Work

The research validates the use of Hamiltonian engineering in augmenting VQE capabilities for frustrated spin systems on NISQ devices. The methods demonstrated herein form a template for scaling quantum simulations to larger, more complex lattices. Potential future directions include more intricate Hamiltonian calibrations, exploration of alternate ansatzes to capture deeper quantum fluctuations, and further integration with emerging quantum error mitigation techniques to expand both the accuracy and scalability of such quantum computations.

Conclusion

This research shifts the paradigm in quantum simulations of strongly correlated materials, particularly in confirming the viability of VQE at scale. The implementation of tailored Hamiltonian engineering combined with noise mitigation techniques opens new possibilities for real-world quantum simulations of complex systems like the Kagome Antiferromagnet. Continued refinements in methodologies and quantum hardware capabilities will increasingly enable reaching the thermodynamic ground state, ultimately furthering our understanding of quantum materials in unprecedented ways.